Thank you for the answers.
FireDac is - to my mind - inspirated by Embarcadero. And they worked with Borland's interbase.
So if Zeos is taken from Interbase, the both FireDac and Zeos may be cousins.
BDB, Dbexpress and FireDac in that order have been the generalized database packages from Embarcadero/Borland.
BDB was DBF and local database oriented (till about D6), DBexpress (D6 - DXE2/3) was more relational database and client server oriented.
I don't know FireDac that well, but one of the objectives was to both work with Firemonkey and VCL, and FireMonkey worked with a different way of databinding (more superficially C# like) called Live Bindings.
Most existing libraries orient themselves to dbexpress, and not FireDac. FPC/Lazarus does not support Firemonkey, not even the most basic work in that direction. Too much closed, and too hard to duplicate, and the same probably goes for firedac. (the VCL was originally a thin layer over WinAPI/GDI, making things more guessable)
The information, that TBStringGrid / DBGrid would not exist now, is from here:
https://wiki.freepascal.org/LCL_Documentation_Roadmap
That is a documentation roadmap, not a component exists roadmap.
As for the namespace issues, see Pascal Dragon's answer. It is annoying because for every new form, the Delphi designer keeps using dotted names and you have to strip them again (hence a tool for that would be nice), but it is currently the best way.